coll.test.sparse | R Documentation |
The Collision test for testing random number generators.
coll.test.sparse(rand, lenSample = 2^14, segments = 2^10, tdim = 2, nbSample = 10, ...)
rand |
a function generating random numbers. its first argument must be
the 'number of observation' argument as in |
lenSample |
numeric for the length of generated samples. |
segments |
numeric for the number of segments to which the interval |
tdim |
numeric for the length of the disjoint t-tuples. |
nbSample |
numeric for the number of repetitions of the test. |
... |
further arguments to pass to function rand |
We consider outputs of multiple calls to a random number generator rand
.
Let us denote by n the length of samples (i.e. lenSample
argument),
k the number of cells (i.e. nbCell
argument).
A collision is defined as when a random number falls in a cell where there are already random numbers. Let us note C the number of collisions
The distribution of collision number C is given by
P(C = c) = ∏_{i=0}^{n-c-1} (k-i)/k *1/(k^c) 2S_n^{n-c},
where 2S_n^{n-c} denotes the Stirling number of the second kind and c=0,..., n-1.
This formula cannot be used for large n since the Stirling number need O(n log(n)) time to be computed. We use a Poisson approximation if n/k < 1/32 and the exact formula otherwise.
The test is repeated nbSample
times and the result of each
repetition forms a row in the output table.
A data frame with nbSample
rows and the following columns.
observed
the observed counts.
p.value
the p-value of the test.
Christophe Dutang, Petr Savicky.
P. L'Ecuyer, R. Simard, S. Wegenkittl, Sparse serial tests of uniformity for random number generators. SIAM Journal on Scientific Computing, 24, 2 (2002), 652-668. doi: 10.1137/S1064827598349033
L'Ecuyer P. (2007), Test U01: a C library for empirical testing of random number generators. ACM Trans. on Mathematical Software 33(4), 22. doi: 10.1145/1268776.1268777
other tests of this package coll.test
, freq.test
, serial.test
, poker.test
,
order.test
and gap.test
ks.test
for the Kolmogorov Smirnov test and acf
for
the autocorrelation function.
# (1) poisson approximation # coll.test.sparse(runif) # (2) exact distribution # coll.test.sparse(SFMT, lenSample=2^7, segments=2^5, tdim=2, nbSample=10) ## Not run: #A generator with too uniform distribution (too small number of collisions) #produces p-values close to 1 set.generator(name="congruRand", mod="2147483647", mult="742938285", incr="0", seed=1) coll.test.sparse(runif, lenSample=300000, segments=50000, tdim=2) #Park-Miller generator has too many collisions and produces small p-values set.generator(name="congruRand", mod="2147483647", mult="16807", incr="0", seed=1) coll.test.sparse(runif, lenSample=300000, segments=50000, tdim=2) ## End(Not run)
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